1. Field of the Invention
The invention is related generally to methods of interpretation of properties of subterranean earth formations using measurements made by a formation evaluation sensor or sensors. Specifically, the invention is directed towards the use of modeling methods that enable the prediction of properties that are not measured by the formation evaluation sensor or sensors.
2. Background of the Art
Oil or gas wells are often surveyed to determine one or more geological, petrophysical, geophysical, and well production properties (“parameters of interest”) using electronic measuring instruments conveyed into the borehole by an umbilical such as a cable, a wireline, slickline, drill pipe or coiled tubing. Tools adapted to perform such surveys are commonly referred to as formation evaluation (FE) tools. These tools use electrical, acoustical, nuclear and/or magnetic energy to stimulate the formations and fluids within the borehole and measure the response of the formations and fluids. The measurements made by downhole instruments are transmitted back to the surface.
In order to reduce the amount of rig time needed for wireline logging, it is common practice to run multiple sensors in a single run. FOCUS™, from Baker Atlas Inc., is a high efficiency premium open hole logging system. All of the downhole instruments have been redesigned, incorporating advanced downhole sensor technology, into shorter, lighter, more reliable logging instruments, capable of providing formation evaluation measurements with the same precision and accuracy as the industry's highest quality sensors, at much higher logging speeds. Logging speeds are up to twice the speed of conventional triple-combo and quad combo logging tool strings. Speeds of up to 3600 ft/hr (1080 m/min) are possible. The logging system may include four standard major open-hole measurements (resistivity, density, neutron, acoustic) plus auxiliary services.
Some petrophysical properties are easily obtained from downhole FE measurements. These include porosity, bulk density, NMR relaxation T1 and T2 spectra, and compressional and shear wave velocities. Other petrophysical properties that are of importance in reservoir evaluation and development are difficult if not impossible to measure. Properties that are difficult or impossible to measure include, for example permeability, relative permeability, resistivity formation factor, capillary pressure, and NMR surface relaxivity. These are typically derived from correlations or petrophysical relationships.
One of the problems with relating the different petrophysical properties of an earth formation to each other is that they are all macroscopically measured quantities that depend ultimately on the microscopic arrangement of the constituents of the earth formation. An early attempt at predicting macroscopic properties based on microscopic models is due to Gassmann (1951) in which the earth formation is modeled as a hexagonal close packing of equal-sized elastic spheres. Based on this simplistic model, it is possible to predict the stress dependence of the packing in terms of the moduli of the constituent spheres.
The earth, of course, is not made out of a hexagonal close packing of equal-size elastic spheres. Finney (1968) measured the spatial coordinates of some 8000 spheres in a random packing of spheres, thereby completely determining the geometry of the microstructure of the packing. This packing may be regarded as a physical model of a clean sediment of well-sorted sand grains. The term “sorting” refers to the distribution of grain sizes: a poorly sorted sandstone has a large range of grain sizes while a well sorted sandstone has grains of substantially the same size. Such sediments can be deposited in a wide spectrum of depositional environments, from nonmarine to basinal deep water. The model developed by Finney is primarily applicable to earth formations comprised of compacted clastic sediments. The term “clastic” refers to rocks made up of fragments of preexisting rocks. Based on the model of Finney, there have been numerous papers that discuss the prediction of formation properties. For example, Bryant and Raikes (1995) used the central core of 3367 spheres in Finney's pack, which has a porosity of 36.2% to try to predict elastic wave velocities in sandstones. In Toumellin et al. (2004), the NMR response of porous rocks was simulated using a continuous, three-dimensional (3D) random-walk algorithm. Diffusion pathways of individual fluid molecules are determined within the 3-D porous model. The method of Toumellin allows the rigorous treatment of T1 and T2 relaxation times with a minimum of assumptions and for arbitrary pulse sequences. Toumellin also discusses the numerical accuracy of the simulation. The results reproduce NMR decay and build-up while accounting for restricted diffusion in porous media, fluid wettabilities, and fluid spatial distributions.
By far the greatest amount of work using pore scale models has been in the area of determination of formation permeability. Valvatne et al. (2003) use pore-scale modeling in which the pore-size distribution is altered to match the capillary injection pressure for different tock types. In addition, for water flooding, contact angles are adjusted to match the measured wettability indices. Gladkikh and Bryant (2004) discuss the use of pore-scale modeling of wetting phase imbibition in porous media. Much of the pioneering work in pore-scale modeling for permeability determination is discussed in papers co-authored by Bryant. What is lacking in prior art is a compact discussion of the interrelation between the different petrophysical parameters that may be determined, and their applicability to hydrocarbon exploration in clastic sediments. The present invention addresses this need.